Additive manufacturing of inverse-designed metadevices

ABSTRACT

A method for creating metadevices includes receiving, at a computing device, one or more boundary conditions for a metadevice. The method also includes processing, with an inverse-design algorithm stored in a memory of the computing device, the one or more boundary conditions to generate a metadevice structure design that satisfies the one or more boundary conditions. The method also includes converting, by a processor of the computing device, the metadevice structure design into a file that is compatible with an additive manufacturing device. The method further includes providing the file of the metadevice structure design to the additive manufacturing device.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the priority benefit of InternationalPatent Application Number PCT/US2018/039433 filed on Jun. 26, 2018,which claims the priority benefit of U.S. Provisional Patent App. No.62/524,715 filed on Jun. 26, 2017, the entire disclosures of which areincorporated by reference herein.

BACKGROUND

Metamaterials refer to electromagnetic (EM) materials that areengineered with a sub-wavelength feature size to exhibit differentproperties than bulk materials. Metadevices are assemblies ofmetamaterials that are engineered to exhibit specific EMfunctionalities. Metasurfaces are a specific class of metadevices with avery thin and planar shape. Metasurfaces have the specific property ofproviding an abrupt phase change to an incoming plane wave, allowingreplication of many classical optical functionalities with a muchthinner structure. Meta-gratings are another class of metadevices thatare periodic. A metalens refers to a metadevice that has the EMfunctionality of a lens.

SUMMARY

A method for creating metadevices includes receiving, at a computingdevice, one or more boundary conditions for a metadevice. The methodalso includes processing, with an inverse-design algorithm stored in amemory of the computing device, the one or more boundary conditions togenerate a metadevice structure design that satisfies the one or moreboundary conditions. The method also includes converting, by a processorof the computing device, the metadevice structure design into a filethat is compatible with an additive manufacturing device. The methodfurther includes providing the file of the metadevice structure designto the additive manufacturing device.

A system for generating metadevices includes a memory configured tostore an inverse-design algorithm, an interface configured to receiveone or more boundary conditions for a metadevice, and a processoroperatively coupled to the memory and the interface. The processor isconfigured to use the inverse-design algorithm to process the one ormore boundary conditions and generate a metadevice structure design thatsatisfies the one or more boundary conditions. The processor is alsoconfigured to convert the metadevice structure design into a file thatis compatible with an additive manufacturing device. The processor isalso configured to provide the file of the metadevice structure designto the additive manufacturing device.

Other principal features and advantages of the invention will becomeapparent to those skilled in the art upon review of the followingdrawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention will hereafter be describedwith reference to the accompanying drawings, wherein like numeralsdenote like elements.

FIG. 1A is a block diagram depicting a polarization splitter in the formof a grating that converts perpendicularly incoming plane waves withparallel and perpendicular polarizations into two different diffractionorders in accordance with an illustrative embodiment.

FIG. 1B is a block diagram depicting a flat metalens device that focusesa plane wave onto a cylindrical wave at a chosen focal point inaccordance with an illustrative embodiment.

FIG. 2A depicts a free-space polarization splitter operational atmillimeter-wave wavelengths in accordance with an illustrativeembodiment.

FIG. 2B depicts plots of simulated power distribution and measured powerdistribution at 33 GHz for the metadevice of FIG. 2A in accordance withan illustrative embodiment.

FIG. 2C depicts simulated Hz field amplitudes for parallel polarizationsat 33 GHz of the metadevice of FIG. 2A in accordance with anillustrative embodiment.

FIG. 2D depicts simulated E field amplitudes for perpendicularpolarizations at 33 GHz in accordance with an illustrative embodiment.

FIG. 2E depicts simulated far-field intensity as a function of theoutput angle and the frequency for parallel polarizations in accordancewith an illustrative embodiment.

FIG. 2F depicts simulated far-field intensity as a function of theoutput angle and the frequency for perpendicular polarizations inaccordance with an illustrative embodiment.

FIG. 2G depicts measured far-field intensity as a function of the outputangle and the frequency for parallel polarizations in accordance with anillustrative embodiment.

FIG. 2H depicts measured far-field intensity as a function of the outputangle and the frequency perpendicular polarizations in accordance withan illustrative embodiment.

FIG. 3A depicts a 15° polarization splitter as a function of the outputangle for a frequency of 33 GHz in accordance with an illustrativeembodiment.

FIG. 3B depicts simulated (dashed lines) and experimental (circles)far-field intensity of the 15° polarization splitter of FIG. 3A as afunction of the output angle for a frequency of 33 GHz in accordancewith an illustrative embodiment.

FIG. 3C depicts a polarization-independent wave bending metadevicehaving a 30° bend as a function of the output angle for a frequency of33 GHz in accordance with an illustrative embodiment.

FIG. 3D depicts simulated (dashed lines) and experimental (circles)far-field intensity of the 30° bend polarization-independent beambending metadevice as a function of the output angle for a frequency of33 GHz in accordance with an illustrative embodiment.

FIG. 4A depicts simulated Hz in the 15° polarization splitter of FIG. 3Awith a perpendicularly incoming plane wave for parallel polarizationsand at a frequency of 33 GHz in accordance with an illustrativeembodiment.

FIG. 4B depicts simulated E in the 15° polarization splitter with aperpendicularly incoming plane wave for perpendicular polarizations andat a frequency of 33 GHz in accordance with an illustrative embodiment.

FIG. 4C depicts simulated far-field intensity maps as a function of theoutput angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations in accordance withan illustrative embodiment.

FIG. 4D depicts experimental far-field intensity maps as a function ofthe output angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations in accordance withan illustrative embodiment.

FIG. 4E depicts simulated far-field intensity maps as a function of theoutput angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for perpendicular polarizations in accordancewith an illustrative embodiment.

FIG. 4F depicts experimental far-field intensity maps as a function ofthe output angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for perpendicular polarizations in accordancewith an illustrative embodiment.

FIG. 5A depicts simulated Hz in the polarization-independent wavebending metadevice of FIG. 3C, with a perpendicularly incoming planewave for parallel polarizations and at a frequency of 33 GHz inaccordance with an illustrative embodiment.

FIG. 5B depicts simulated E in the metadevice of FIG. 3C with aperpendicular incoming plane wave for perpendicular polarizations and ata frequency of 33 GHz in accordance with an illustrative embodiment.

FIG. 5C depicts simulated far-field intensity maps as a function of theoutput angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations of the metadeviceof FIG. 3C, in accordance with an illustrative embodiment.

FIG. 5D depicts experimental far-field intensity maps as a function ofthe output angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations in the metadeviceof FIG. 3C, in accordance with an illustrative embodiment.

FIG. 5E depicts simulated far-field intensity maps as a function of theoutput angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for perpendicular polarizations in themetadevice of FIG. 3C, in accordance with an illustrative embodiment.

FIG. 5F depicts experimental far-field intensity maps as a function ofthe output angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for perpendicular polarizations in themetadevice of FIG. 3C, in accordance with an illustrative embodiment.

FIGS. 6A-6F show a comparison between the performance of theinverse-designed device (FIGS. 6A-6C) and a blazed grating (FIGS. 6D-6F)optimized to bend electromagnetic radiation by 30° independently of thepolarization in accordance with illustrative embodiments.

FIG. 7A depicts a plot of simulated power distribution along the x-yplane for a short-range metalens at 38 GHz in accordance with anillustrative embodiment.

FIG. 7B depicts a plot of simulated power distribution along the x-yplane for a long-range metalens at 38 GHz in accordance with anillustrative embodiment.

FIG. 7C depicts a measured spatial power distribution in the x-y planefor the short-range metalens at 38 GHz in accordance with anillustrative embodiment.

FIG. 7D depicts a measured spatial power distribution in the x-y planefor a long-range lens at 38 GHz in accordance with an illustrativeembodiment.

FIG. 7E shows a cross-section of the simulated (lines) and measured(circles) power along the white dashed lines on the maps for the firstlens in accordance with an illustrative embodiment.

FIG. 7F shows a cross-section of the simulated (lines) and measured(circles) power along the white dashed lines on the maps for the secondlens in accordance with an illustrative embodiment.

FIG. 8A depicts a simulated E field amplitude map along the x-y plane ata frequency of 38 GHz, with the black lines showing the contour of thefirst metalens in accordance with an illustrative embodiment.

FIG. 8B depicts a simulated E field amplitude map along the x-y plane ata frequency of 38 GHz, with the black lines showing the contour of thesecond metalens in accordance with an illustrative embodiment.

FIG. 9A depicts simulated electromagnetic power maps along the x-y planeat the output of the first metalens at a frequency of 30 GHz inaccordance with an illustrative embodiment.

FIG. 9B depicts simulated electromagnetic power maps along the x-y planeat the output of the second metalens at a frequency of 30 GHz inaccordance with an illustrative embodiment.

FIG. 9C depicts experimental electromagnetic power maps along the x-yplane at the output of the first metalens at a frequency of 30 GHz inaccordance with an illustrative embodiment.

FIG. 9D depicts experimental electromagnetic power maps along the x-yplane at the output of the second metalens at a frequency of 30 GHz inaccordance with an illustrative embodiment.

FIG. 9E depicts a cross-section of the power along the dashed lines onthe maps for the first metalens in accordance with an illustrativeembodiment.

FIG. 9F depicts a cross-section of the power along the dashed lines onthe maps for the second metalens in accordance with an illustrativeembodiment.

FIG. 10A is an electron microscope picture showing an infrared devicemade with SU-8 polymer and printed with a 3D-printer in accordance withan illustrative embodiment.

FIG. 10B depicts a larger plastic millimeter wave device having asimilar shape to the device in FIG. 10A, in accordance with anillustrative embodiment.

FIG. 11 is a flow diagram depicting a process for creating a metadevicein accordance with an illustrative embodiment.

FIG. 12 is a block diagram of a computing system for generatingmetadevices in accordance with an illustrative embodiment.

DETAILED DESCRIPTION

Described herein is a platform for the design and fabrication of highefficiency dielectric metadevices. The metadevices are designed by wayof inverse electromagnetic design computational methods, and in oneembodiment the metadevices are fabricated using additive manufacturing.The metadevices described herein are designed to provide completecontrol of the phase and the polarization of an incident wave. Inparticular, the embodiments described herein can be used to createmillimeter-wave frequency metadevices that perform polarizationsplitting, beam bending, and focusing with high efficiency over a broadrange of wavelength range. The methods described herein are scalable andcan also be extended for the design and fabrication of electromagneticand photonic metadevices spanning microwave to optical frequencies.

Conventional optical elements that control the polarization, phase, andamplitude of electromagnetic (EM) radiation include lenses, polarizers,beamsplitters, and mirrors. Such optical elements are typicallyengineered at a scale larger than the wavelength. Within the last twodecades, a significant amount of research has been devoted tounderstanding light-matter interactions, designing novel materials, anddesigning electromagnetic devices with subwavelength feature sizes.Metamaterials, and more generally materials composed of nanostructureswith subwavelength feature size, have emerged as a viable platform tomanipulate electromagnetic radiation in an unconventional manner. Inparticular, photonic crystals and negative-index materials are used toachieve sub-diffraction lensing. More recently, metasurfaces have gainedsubstantial interest due to their ability to perform opticalfunctionalities such as lensing, holograms, and beam shaping within anextremely thin layer.

Metasurfaces are formed of discrete subwavelength resonant elementsarranged in a specific manner to impart a desired global phase change toan incoming electromagnetic wave. Using subwavelength thick metasurfacesto control phase, amplitude, and polarization is a promising routetowards building miniature optical devices. However, existing design andfabrication methods suffer from several drawbacks prohibiting thepotential of using metasurfaces to replace conventional bulk opticalelements. Initial metasurface designs utilized plasmonic metals thatexhibited high optical losses, leading to relatively low efficiency.Additionally, although metals can be replaced with high-index dielectricmaterials such as silicon, such metasurfaces often rely on Mie-typeresonances that result in a narrow wavelength operation range.

Typically, metasurface design starts with identification of an opticalresonator with a well-defined geometrical shape, such as a triangle,rectangle, ellipse, V-antenna, etc. Phase information is then calculatedfor various geometrical parameters such as radius, width, orientation,etc. However, metadevices which are based on traditionally designedultrathin metasurfaces often yield polarization dependency andnarrowband optical response, as their design relies on subwavelengthoptical resonators.

Described herein is an inverse electromagnetic design method to formhigh-efficiency (e.g., >60%), broadband (e.g., Δλ/λ>25%, where λ iswavelength), dielectric-based thin (e.g., ≤2λ) electromagneticmetadevices overcoming the aforementioned limitations of traditionalmetadevices. In alternative embodiments, the efficiency value, broadbandvalue, and/or thickness of metadevices described herein may differ fromthe values identified above. The metadevices created using the processesdescribed herein can be non-resonant structures which have a very broadresponse as compared with traditional devices. Also, the metadevicesdescribed herein can allow manipulation of light/radiation in plane.

Inverse-design refers to the use of an algorithm to design differenttypes of devices. Inverse-design algorithms include objective-firstalgorithms, topology optimization algorithms, brute force algorithms,genetic algorithms, etc. The present description focuses primarily onobjective-first inverse design, but the embodiments disclosed herein arenot so limited and other types of inverse-design may also be used. Byusing an optimization algorithm that is coupled with an electromagneticsimulation, a complex dielectric structure that provides a desired phasechange distribution for a desired optical functionality can be designed.As used herein, inverse-design refers to a process in which a computingsystem computationally designs a device based on a set offunctionalities that one wants the device to achieve. In the context ofmetadevices, a set of electromagnetic input and output values isdesignated, and the computing system designs a metadevice that satisfiesthose values.

As discussed herein, the inventors have also identified benefits tousing an additive manufacturing process, such as 3D printing, to createoptical metadevices that are designed using an inverse designmethodology. The use of such additive manufacturing allows creation ofdevices which cannot be fabricated using traditional removal techniquessuch as milling. In one embodiment, the 3D-printed devices can be madeof high impact polystyrene (HIPS) and fabricated with a consumer3D-printer based on fused deposition modeling. In alternativeembodiments, a different fabrication material and/or technique may beused. The HIPS material has low cost and very low attenuation in themicrowave and millimeter-wave wavelengths, with a loss-tangent measuredto be tan δ<0.003 over the 26-38 GHz band. The real part of thedielectric constant of HIPS was ε′≈2.3 (n≈1.52) in this band, which canbe used as a constraint in the inverse-design algorithm to design binarydevices made of air (ε=1) and HIPS (ε=2.3). Because of the low index,the phase between the input and output is approximately proportional tothe effective thickness of the polymer. Therefore, in order to allow a2π phase shift between a part full of polymer and a part full of air,the device thickness should obey Equation 1 below. In this particularembodiment, Equation 1 indicates that the thickness of the metadevicesshould be slightly larger than 2π.

$\begin{matrix}{{\Delta\varphi} = {{2\; {\pi ( {n - 1} )}\frac{t}{\lambda}} = {{2\; \pi \times 0.52 \times \frac{t}{\lambda}} \geq {2\; \pi}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In order to test the electromagnetic properties of the createdmetadevices, a vector network analyzer (VNA) can be used to generate aninput signal transmitted through a high-gain horn antenna placed faraway from the sample (distance>100λ) in order to produce a plane waveperpendicularly incident to the input surface. The metadevice issurrounded by radar absorbing material to prevent the signal from goingaround it. For the polarization splitters and beam bending metadevices,the transmitted power was measured in the far-field (>100λ) with a lowgain horn antenna as a function of the angle between −40° and 40° by 2°steps, and as a function of the frequency between 26 GHz (11.5 mm) and38 GHz (7.9 mm). For the created metalenses, the transmitted power canbe measured in the near-field with a probe antenna scanned in the x-yplane at the output of the devices. The results of the measurementstaken from actual metadevices created in accordance with the embodimentsdescribed herein are discussed below with reference to the figures.

The design, fabrication, and characterization of ˜λ thick metadevicesfor bending, polarization splitting, and focusing of EM radiation atmillimeter-wave frequencies are demonstrated herein. The methodologiescan, however, be used to create a number of different metadevices,including devices operating in near-infrared for telecommunications,devices operating in mid/long-infrared and THz for chemical sensing andIR imaging, devices operating microwave and millimeter wave for wirelesscommunications and military applications, dielectric antennas with lowloss optimized for specific beam shaping between near-infrared andmillimeter waves, ultra-thin lenses for beam focusing in the near-filed,polarization splitters, wavelength separators, on-chip control of lightpropagation (near-IR), passive optical devices for THz radiation, etc.

FIGS. 1A and 1B are schematics for an illustrative inverseelectromagnetic design approach for designing free-space metadevices.More specifically, FIG. 1A is a block diagram depicting a free-spacepolarization splitter meta-grating that bends parallel and perpendicularpolarizations to opposite diffraction orders in accordance with anillustrative embodiment. The design and fabrication processes describedherein can also be used to create a meta-grating that bends bothpolarizations to the same diffraction order. FIG. 1B is a block diagramdepicting a flat metalens device that focuses a plane wave onto acylindrical wave at a chosen focal point in accordance with anillustrative embodiment. As discussed in more detail below, the desiredoptical functionality of the metadevices is defined as a set of inputand output conditions at the boundaries of the design space.

As part of the inverse design process, the objective-first algorithm canbe used, and the electromagnetic wave equation is treated as anoptimization problem. The electric field, E and the dielectricpermittivity, ε, can be solved for using Eq. 2 below, based on a desiredinput and output electromagnetic field distribution.

$\begin{matrix}{{\min\limits_{ɛ,E}{\nabla{\times {\nabla{\times E}}}}} - {w^{2}ɛ\; E}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Such an optimization problem is non-convex. Therefore, there is nogeneral method to find the optimum solution. However, suitable solutionsthat satisfy desired functionality with acceptable performance can bereached. An on-chip wavelength splitter and an optical diode have beensuccessfully demonstrated using such an inverse electromagnetic designapproach.

Bending and polarization splitting are achieved with meta-gratings thatconvert an input plane wave to an output plane wave with a differentdiffraction order than m=0, with periodic boundary conditions along thex-axis. For metalenses, one goal is to focus a plane wave at a desiredfocal length. Thus, in one embodiment, the output is chosen to be acylindrical wave centered at a specific location. Metalenses do notperform like a grating. Thus, in the case of metalenses, the boundaryconditions are set to be a Perfectly Matched Layer (PML) along the xdirection. In one embodiment, the inverse design described herein istwo-dimensional, and it is therefore assumed that metadevices haveinfinite height along the z axis. In practice, the fabricated devicesare ≈10λ thick. However, in alternative embodiments, differentthicknesses may be used such as 5λ, 7λ, 12λ, etc.

Inverse-designed metadevices are realized using additive manufacturing,which is commonly referred to as 3D-printing. This bottom-up approachallows the fabrication of complex devices with high aspect ratio.Furthermore, 3D-printing is a scalable method, with resolutions rangingfrom ˜100 nm to 1 ˜mm or larger, allowing the fabrication ofelectromagnetic devices with applications from visible light tomillimeter waves and microwaves. As a result, the proposed devicesdescribed herein can be practically realized for microwave andmillimeter waves with polymer-based 3D-printing.

FIG. 2A depicts a free-space polarization splitter operational atmillimeter-wave wavelengths in accordance with an illustrativeembodiment. More specifically, FIG. 2A depicts a schematic drawing(left) and a top-view photograph (right) of a 3D printed 30°polarization splitter. The photograph (right) of the 3D-printedmetadevice shown next to the computer-generated pattern (left) in FIG.2A illustrates the high fidelity of the 3D-printing process. The dashedline rectangle of FIG. 2A indicates a unit cell of the grating. Themetadevice of FIG. 2A deflects a normal incident plane-wave polarizedalong they (parallel) and z (perpendicular) directions into m=+1 andm=−1 diffraction orders, respectively, with high efficiency and over abroad bandwidth. With respect to design parameters, the metadevice ofFIG. 2A was assumed to be periodic in the y-direction and infinite alongthe z direction. The width of the metadevice was chosen to be ˜2λ, butcan be different in alternative embodiments. The periodicity, L, alongthey axis was determined by the deflection angle θ of the desireddiffraction order m (here, m=±1 for all devices), following the gratingequation L sin θ=mλ. The metadevice was designed and optimized for anoperation frequency of 33 GHz, λ=9.1 mm, and a deflection angle ofθ=±30°, for which L=1.8 cm. The inverse-design algorithm generated abinary refractive index distribution of dielectric and air that was thenprinted with dimensions of 2 cm×7.2 cm×8 cm.

Far-field angular transmission through the actual metadevice of FIG. 2Awas measured to verify predicted polarization splitting behavior. FIG.2B depicts plots of simulated power distribution and measured powerdistribution at 33 GHz in accordance with an illustrative embodiment. InFIG. 2B, dashed lines represent simulated values and circles representmeasured values of far-field power as a function of deflection angle forboth polarizations. In the metadevice of FIG. 2A, a plane wave withparallel polarization was observed to bend at an angle of θ32 +30°,whereas perpendicular polarization was deflected with an angle ofθ=−30°. The total power transmitted by the metadevice at 33 GHz wasmeasured to be 76% for the parallel polarization and 54% for theperpendicular polarization, which is lower than the simulated values of90% due to structural imperfections. The rejection ratio, defined as theratio between the peak intensity and the maximum intensity outside themain peak, was experimentally found to be 5.2 dB and 7.0 dB for paralleland perpendicular polarizations, respectively, which is close to thesimulation values of 6.6 dB and 9.3 dB, respectively.

Full-field electromagnetic simulations were performed to calculate theelectromagnetic properties of the metadevice of FIG. 2A. FIG. 2C depictssimulated Hz field amplitudes for parallel polarizations at 33 GHz inaccordance with an illustrative embodiment. FIG. 2D depicts simulated Efield amplitudes for perpendicular polarizations at 33 GHz in accordancewith an illustrative embodiment. Spatial electromagnetic fielddistribution provides a clear picture of how the EM wave propagatesinside the metadevice. For example, the metadevice of FIG. 2A presents adielectric filling fraction gradient along the y-direction between apart mostly filled with dielectric (ε=2.3), where the phase was shiftedby 6π, and a part mostly void (ε=1.0) where the phase was shifted byonly 4π, allowing a 2π phase shift in the y-direction. The polarizationsplitting was a result of the different phase change response of thedifferent polarizations resulting from the complex dielectric shape ofthe device.

Although 33 GHz was chosen to be the optimum frequency with highestefficiency in the inverse-design algorithm, broad operation bandwidthwas observed that spanned the entire measurement range, which wasenabled by the inverse-design method favoring non-resonant dielectricstructures. As such, in alternative embodiments, different frequenciesmay be used to design metadevices in accordance with the inverse-designalgorithm. FIG. 2E depicts simulated far-field intensity as a functionof the output angle and the frequency for parallel polarizations inaccordance with an illustrative embodiment. FIG. 2F depicts simulatedfar-field intensity as a function of the output angle and the frequencyfor perpendicular polarizations in accordance with an illustrativeembodiment. FIG. 2G depicts measured far-field intensity as a functionof the output angle and the frequency for parallel polarizations inaccordance with an illustrative embodiment. FIG. 2H depicts measuredfar-field intensity as a function of the output angle and the frequencyperpendicular polarizations in accordance with an illustrativeembodiment. As illustrated, the simulations and measurements agreedwell, apart from minor differences that can be explained by the finitenumber of periods in the printed structures as well as an imperfectplane wave input.

In order to demonstrate the versatility and flexibility of theinverse-design approach, two additional metadevices that bendmillimeter-waves were designed and fabricated. FIG. 3A depicts apolarization splitter with a 15° bending angle as a function of theoutput angle for a frequency of 33 GHz in accordance with anillustrative embodiment. Similar to the 30° splitter, the metadevice ofFIG. 3A presents a gradient of dielectric filling fraction along they-direction with a larger periodicity (L=3.5 cm) to favor a smallerbending angle. FIG. 3B depicts simulated (dashed lines) and experimental(circles) far-field intensity of the 15° polarization splitter of FIG.3A as a function of the output angle for a frequency of 33 GHz inaccordance with an illustrative embodiment. The measured rejectionratios for the 15° splitter are 8.2 dB and 10.6 dB for parallel andperpendicular polarizations, respectively.

The designs, simulated fields, and broadband far-field data of themetadevice of FIG. 3A are depicted in FIG. 4. In the case ofperpendicular polarization, a wave propagating along the y-direction wascreated in the metadevice, changing its behavior compared to parallelpolarization. For example, FIG. 4A depicts simulated H_(z) in the 15°polarization splitter with a perpendicularly incoming plane wave forparallel polarizations and at a frequency of 33 GHz in accordance withan illustrative embodiment. FIG. 4B depicts simulated E_(z) in the 15°polarization splitter with a perpendicularly incoming plane wave forperpendicular polarizations and at a frequency of 33 GHz in accordancewith an illustrative embodiment. FIG. 4C depicts simulated far-fieldintensity maps as a function of the output angle between −40° and 40°and as a function of the frequency between 26 GHz and 38 GHz forparallel polarizations in accordance with an illustrative embodiment.FIG. 4D depicts experimental far-field intensity maps as a function ofthe output angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations in accordance withan illustrative embodiment. FIG. 4E depicts simulated far-fieldintensity maps as a function of the output angle between −40° and 40°and as a function of the frequency between 26 GHz and 38 GHz forperpendicular polarizations in accordance with an illustrativeembodiment. FIG. 4F depicts experimental far-field intensity maps as afunction of the output angle between −40° and 40° and as a function ofthe frequency between 26 GHz and 38 GHz for perpendicular polarizationsin accordance with an illustrative embodiment.

In addition to a polarization beam-splitter, a polarization-independentmillimeter-wave bending metadevice was also designed and realized, inwhich both polarizations are bent to the same diffraction order. FIG. 3Cdepicts a polarization-independent wave bending metadevice having a 30°bend as a function of the output angle for a frequency of 33 GHz inaccordance with an illustrative embodiment. FIG. 3D depicts simulated(dashed lines) and experimental (circles) far-field intensity of the 30°bend polarization-independent beam bending metadevice as a function ofthe output angle for a frequency of 33 GHz in accordance with anillustrative embodiment. As indicated in FIG. 3D, the results show verygood agreement between theory and experiment.

The designs, simulated fields, and broadband far-field data for thepolarization-independent wave bending metadevice of FIG. 3C are shown inFIG. 5. Specifically, FIG. 5A depicts simulated Hz in thepolarization-independent wave bending metadevice of FIG. 3C, with aperpendicularly incoming plane wave for parallel polarizations and at afrequency of 33 GHz in accordance with an illustrative embodiment. FIG.5B depicts simulated E_(z) in the metadevice of FIG. 3C with aperpendicular incoming plane wave for perpendicular polarizations and ata frequency of 33 GHz in accordance with an illustrative embodiment.FIG. 5C depicts simulated far-field intensity maps as a function of theoutput angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations of the metadeviceof FIG. 3C, in accordance with an illustrative embodiment. FIG. 5Ddepicts experimental far-field intensity maps as a function of theoutput angle between −40° and 40° and as a function of the frequencybetween 26 GHz and 38 GHz for parallel polarizations in the metadeviceof FIG. 3C, in accordance with an illustrative embodiment. FIG. 5Edepicts simulated far-field intensity maps as a function of the outputangle between −40° and 40° and as a function of the frequency between 26GHz and 38 GHz for perpendicular polarizations in the metadevice of FIG.3C, in accordance with an illustrative embodiment. FIG. 5F depictsexperimental far-field intensity maps as a function of the output anglebetween −40° and 40° and as a function of the frequency between 26 GHzand 38 GHz for perpendicular polarizations in the metadevice of FIG. 3C,in accordance with an illustrative embodiment.

Although polarization-independent bending of EM radiation can beachieved with a triangular blazed grating, it has been demonstrated thatsuch gratings deflect a significant amount of power to the higherdiffraction orders. On average, from 26 to 38 GHz, the inverse-designedmetadevices reduce the amount of power sent into undesired diffractionorders by a factor of 2.8 for parallel polarization and 2.0 forperpendicular polarization, when compared to a blazed grating withsimilar thickness. FIGS. 6A-6F show a comparison between the performanceof the inverse-designed device (FIGS. 6A-6C) and a blazed grating (FIGS.6D-6F) optimized to bend electromagnetic radiation by 30° independentlyof the polarization in accordance with illustrative embodiments. Thesimulated far-field intensities are represented for angles from −80° to80° and for frequencies from 26 GHz to 38 GHz for perpendicularpolarizations (FIGS. 6B and 6E) and parallel polarizations (FIGS. 6C and6F). As can be seen, the inverse-designed metadevice transmits a muchlower power to undesired grating orders (23% for perpendicularpolarization and 18% for parallel polarization) than the blazed grating(47% for perpendicular polarization and 51% for parallel polarization).Simulated rejection ratios at 32 GHz are 10.1 dB (perpendicularpolarization) and 12.4 dB (parallel polarization) for theinverse-designed bend, compared to 6.6 dB (perpendicular polarization)and 3.8 dB (parallel polarization) for the triangular grating.

Flat metalenses can also be designed using the inverse-design algorithmdescribed herein. Such metalenses are used to focus an incoming planewave onto a focal point, as depicted in FIG. 1B. Two differentmetalenses were designed and fabricated with focal lengths 2λ and 15λaway from the surface of the device. Both lenses were optimized andscaled for operation around 38 GHz=7.9 mm). The first metalens was 1.5cm wide and 10 cm long, the second metalens was 2.5 cm wide and 15 cmlong, and both metalenses were 10 cm tall. In alternative embodiments,different focal lengths, operating frequency, and/or dimensions may beused to create metalenses.

FIG. 7 shows a depiction of each metalens and the correspondingcomputer-generated design in accordance with an illustrative embodiment.The electromagnetic behavior of both metalens devices was simulated witha perpendicularly polarized incoming plane wave. FIG. 7A depicts a plotof simulated power distribution along the x-y plane for a short-rangemetalens at 38 GHz in accordance with an illustrative embodiment. FIG.7B depicts a plot of simulated power distribution along the x-y planefor a long-range metalens at 38 GHz in accordance with an illustrativeembodiment. A 2D scan of the transmitted power was performed after themetalenses were used, using a millimeter-wave probe antenna positionedat z=5 cm. FIG. 7C depicts a measured spatial power distribution in thex-y plane for the short-range metalens in accordance with anillustrative embodiment. FIG. 7D depicts a measured spatial powerdistribution in the x-y plane for a long-range lens in accordance withan illustrative embodiment. Simulated and measured spatial intensitydistribution for the metalenses closely matched, with smalldiscrepancies due to the imperfect plane wave input, and minordifferences between the ideal designs and the fabricated devices. Asexpected, the first metalens device focused EM radiation 1.5 cm (˜2λ)away from the device while the second metalens device had a focal pointlocated 12 cm (˜15λ) away, with theoretical numerical apertures (NA) of0.82 and 0.53, respectively. The full-width-at-half-maximum (FWHM) ofboth devices were, respectively, 0.5 cm and 1.1 cm, which corresponds topractical NA of 0.8 and 0.36, respectively. These values are close tothe theoretical values. The metalens devices showed broadband focusingbehavior from 28 GHz to 40 GHz.

In FIGS. 7A and 7C, the input plane wave is generated by a horn antenna1 m away on the left of the device while the output is measured with aprobe antenna scanned along a 9×10 cm x-y plane for the first lens. InFIGS. 7B and 7D, the input plane wave is generated by a horn antenna 1 maway on the left of the device while the output is measured with a probeantenna scanned along a 14×15 cm plane for the second lens. Schematicsand a picture of the 3D-printed metalenses are shown next to thesimulated and experimental maps, respectively. FIG. 7E shows across-section of the simulated (lines) and measured (circles) poweralong the white dashed lines on the maps for the first lens inaccordance with an illustrative embodiment. FIG. 7F shows across-section of the simulated (lines) and measured (circles) poweralong the white dashed lines on the color maps for the second lens inaccordance with an illustrative embodiment.

FIG. 8A depicts a simulated E field amplitude map along the x-y plane ata frequency of 38 GHz, with the black lines showing the contour of thefirst metalens in accordance with an illustrative embodiment. FIG. 8Bdepicts a simulated E_(z) field amplitude map along the x-y plane at afrequency of 38 GHz, with the black lines showing the contour of thesecond metalens in accordance with an illustrative embodiment. In FIG.8A, the first metalens has a focal distance of 2λ. In FIG. 8B, thesecond metalens has a focal distance of 15λ.

Measured and simulated intensity profiles for the first and secondmetalenses operated at 30 GHz are provided in FIG. 9. Specifically, FIG.9A depicts simulated electromagnetic power maps along the x-y plane atthe output of the first metalens at a frequency of 30 GHz in accordancewith an illustrative embodiment. FIG. 9B depicts simulatedelectromagnetic power maps along the x-y plane at the output of thesecond metalens at a frequency of 30 GHz in accordance with anillustrative embodiment. FIG. 9C depicts experimental electromagneticpower maps along the x-y plane at the output of the first metalens at afrequency of 30 GHz in accordance with an illustrative embodiment. FIG.9D depicts experimental electromagnetic power maps along the x-y planeat the output of the second metalens at a frequency of 30 GHz inaccordance with an illustrative embodiment. FIG. 9E depicts across-section of the power along the dashed lines on the maps for thefirst metalens in accordance with an illustrative embodiment. FIG. 9Fdepicts a cross-section of the power along the dashed lines on the mapsfor the second metalens in accordance with an illustrative embodiment.

Although one focus of the present application is on millimeter wavedevices which can be printed with a consumer 3D-printer, the methodsdescribed herein can be extended to any type of electromagneticradiation (e.g., UV, visible, Infrared, TeraHertz, mmWave, microwave,radio, etc.) as long as the right materials are used, the devices arescaled properly, and the 3D-printing fabrication method is capable ofprinting at the given scale. As one example, the methods and systemsdescribed herein can be used to fabricate devices 3,000 or more timessmaller than the proof-of-concept devices described herein. Todemonstrate this scalability, FIG. 10A is an electron microscope imageshowing an infrared device made with SU-8 polymer and printed with a3D-printer in accordance with an illustrative embodiment. FIG. 10Bdepicts a larger plastic millimeter wave device having a similar shapeto the device in FIG. 10A, in accordance with an illustrativeembodiment. It is expected that the properties of the devices of FIG.10A (i.e., infrared) and 10B (i.e., mmWave) are exactly the same.

FIG. 11 is a flow diagram depicting a process for creating a metadevicein accordance with an illustrative embodiment. In alternativeembodiments, fewer, additional, and/or different operations may beperformed. Also, the use of a flow diagram is not meant to be limitingwith respect to the order of operations performed. In an operation 1100,a type of metadevice to be created is determined. The metadevice can bean optical metadevice, a mechanical metadevice, an acoustic metadevice,or any other type of metadevice. Examples of types of an opticalmetadevice include a lens to focus radiation at a specific distance, apolarization splitter to send different types of radiation in differentdirections, a polarization or wavelength filter that allows onepolarization or wavelength to transmit while the other(s) are reflected,a bending device, a hologram device, a beam-shaping device to shapeGaussian beams, Bessel beams, etc., an antenna, an electromagneticbandgap device, etc.

In an operation 1105, boundary conditions (or parameters) for themetadevice are determined. For example, the boundary conditions for alens can include a focal distance and/or a numerical aperture, boundaryconditions for a polarization splitter can include the angle(s) ofdeflection, boundary conditions for a filtering device include thepolarization and/or wavelength that is to be filtered, and the boundaryconditions for a bending device include the angle at which the radiationis to be bent. Additionally, boundary conditions for a hologram includehologram shape, wavelength, and polarization, boundary conditions for abeam-shaping device include the beam divergence, the boundary conditionsfor an antenna include gain and directivity, and boundary conditions foran EM bandgap device include a range of wavelengths in the bandgap.Additional boundary conditions (or parameters) for the above-describedoptical metadevices can include permittivity and permeability (whichdictate the type of material used to form the device), device size, andwhether the device is periodic or not, among others.

In an operation 1110, the boundary conditions for the determinedmetadevice are provided to an inverse-design algorithm in the form of anobjective-first inverse-design algorithm. In alternative embodiments,different types of inverse-design approaches may be used. Theinverse-design algorithm (or other algorithm) is configured to generatea design for the metadevice that satisfies all of the specified boundaryconditions.

In an operation 1115, the metadevice structure design is received fromthe inverse-design algorithm. In an illustrative embodiment, an outputfrom the inverse-design algorithm is in the form of a matrixrepresenting a map of the permittivity and permeability values in atwo-dimensional space. In alternative embodiments, the matrix values canbe in a three-dimensional space.

In an operation 1120, the metadevice structure design is converted intoa 3D-printer compatible file. The permittivity values in the matrix canoriginally have continuous values. In the conversion operation (1120),the originally continuous permittivity values are converted into amatrix of binary values representing the presence or absence ofmaterial. This matrix of binary values is converted into a black andwhite image using computer software such as OriginPro. Alternatively, adifferent type of software may be used. The black and white image istreated with image processing software to smooth any edges that arepixelated. The black and white image is also vectorized such that onlythe edges are kept. The vectorization can be performed using Autotracer,or alternatively a different vectorization tool may be used. In oneembodiment, the vectorized image is converted into a .dxf format.Alternatively, other formats can be used. The vectorized image structureis converted into a full 2-D structure using a layout editor, and the2-D structure file (e.g., .dxf file) is extruded to convert it into a3-D structure having a given thickness. The extrusion can be performedby importing the .dxf file into Fusion 360 software, or alternativelydifferent software may be used. A result of the extrusion is a .stl filein an illustrative embodiment. The .stl file is imported into a program(e.g., Cura) that converts the .stl file into a .gcode file, which is aformat that describes the actions that a 3-D printer must take to printthe structure.

In an operation 1125, the 3D-printer compatible file (e.g., .gcode file)is provided to a 3D-printer. In an operation 1130, the metadevice isprinted with the 3D-printer. Any type of 3D-printer capable of theprinting at the desired scale may be used.

As described herein, a platform for the design and fabrication of novelmillimeter-wave and other metadevices using an inverse electromagneticdesign algorithm and additive manufacturing is provided. The proposeddesign and fabrication method can be generalized to differentelectromagnetic and photonic devices, in which the desired responses canbe defined as input and output electromagnetic field distributions.Although metadevices at millimeter-wave range are realized anddemonstrated, due to scalability of Maxwell's equations, similar devicescan be designed to operate at visible to microwave frequency ranges,provided that a low-loss dielectric material can be fabricated withsubwavelength feature sizes. The presented platform addresses the needfor rapid versatile design and prototyping of compact, low-cost,low-loss, and broadband components that can be easily integrated intocomplex electromagnetic systems. Additionally, acoustic and mechanicalequations are similar to Maxwell's equations, and the inverse-designalgorithms described herein can be extended to the design of acousticand/or mechanical devices.

In an illustrative embodiment, any of the operations described hereinmay be performed by a computing system that includes a memory,processor, user interface, transceiver, and any other computingcomponents. The operations can be stored as computer-readableinstructions on a computer-readable medium such as the computer memory.Upon execution by the processor, the computer-readable instructions areexecuted as described herein.

FIG. 12 is a block diagram of a computing system 1200 for generatingmetadevices in accordance with an illustrative embodiment. The computingsystem 1200 includes a processor 1205, an operating system 1210, amemory 1215, an input/output (I/O) system 1220, a network interface1225, and a design algorithm 1230. Additionally depicted is a network1235 and an additive manufacturing device 1240. In alternativeembodiments, the computing system 1200 may include fewer, additional,and/or different components. The components of the computing systemcommunicate with one another via one or more buses or any otherinterconnect system. The computing system 1200 can be incorporated intoa device such as a laptop computer, desktop computer, smart phone,tablet, workstation, server, imaging device, a manufacturing device suchas the additive manufacturing device 1240, etc.

The processor 1205 can be any type of computer processor known in theart, and can include a plurality of processors and/or a plurality ofprocessing cores. The processor 1205 can include a controller, amicrocontroller, an audio processor, a graphics processing unit, ahardware accelerator, a digital signal processor, etc. Additionally, theprocessor 1205 may be implemented as a complex instruction set computerprocessor, a reduced instruction set computer processor, an x86instruction set computer processor, etc. The processor is used to runthe operating system 1210, which can be any type of operating system.The processor 1205 uses the design algorithm 1230 to process boundaryconditions and generate a metadevice structure design. The processor1205 also converts the metadevice structure design into a file that iscompatible with the additive manufacturing device 1240, and provides thefile of the metadevice structure design to the additive manufacturingdevice.

The operating system 1210 is stored in the memory 1215, which is alsoused to store programs, user data, network and communications data,peripheral component data, and the design algorithm 1230. The memory1215 can be one or more memory systems that include various types ofcomputer memory such as flash memory, random access memory (RAM),dynamic (RAM), static (RAM), a universal serial bus (USB) drive, anoptical disk drive, a tape drive, an internal storage device, anon-volatile storage device, a hard disk drive (HDD), a volatile storagedevice, etc.

The I/O system 1220 is the framework which enables users and peripheraldevices to interact with the computing system 1200. The I/O system 1220can include a mouse, a keyboard, one or more displays, a speaker, amicrophone, and/or any other user interfaces that allow the user tointeract with and control the computing system 1200. The I/O system 1220also includes circuitry and a bus structure to interface with peripheralcomputing devices such as power sources, USB devices, peripheralcomponent interconnect express (PCIe) devices, serial advancedtechnology attachment (SATA) devices, high definition multimediainterface (HDMI) devices, proprietary connection devices, etc.

The network interface 1225 includes transceiver circuitry that allow thecomputing system to transmit and receive data to/from other devices suchas remote computing systems, servers, websites, etc. The networkinterface 1225 enables communication through a network 1235, which canbe one or more communication networks. The network 1235 can include acable network, a fiber network, a cellular network, a wi-fi network, alandline telephone network, a microwave network, a satellite network,etc. The network interface 1225 also includes circuitry to allowdevice-to-device communication such as Bluetooth® communication. Theadditive manufacturing device 1240, which can be a 3-D printer, is usedto generate a metadevice based on a design file received from thecomputing system 1200. The additive manufacturing device 1240 canreceive the design file through the network 1235 in one embodiment.Alternatively, the additive manufacturing device 1240 can receive thedesign file via a direct connection between the computing system 1200and the additive manufacturing device 1240. In another embodiment, theadditive manufacturing device 1240 can be incorporated into thecomputing system 1200, or vice versa.

The design algorithm 1230 can include any type(s) of design algorithmwhich can be used to form a metadevice based on user specifications(i.e., boundary conditions, etc.). In an illustrative embodiment, thedesign algorithm is an inverse-design algorithm. In alternativeembodiments, a different type of algorithm may be used. The processor1205 uses the design algorithm to process boundary conditions andgenerate a metadevice structure design. In an alternative embodiment,the design algorithm 1230 can be remote or independent from the rest ofthe computing system 1200, but in communication therewith.

The word “illustrative” is used herein to mean serving as an example,instance, or illustration. Any aspect or design described herein as“illustrative” is not necessarily to be construed as preferred oradvantageous over other aspects or designs. Further, for the purposes ofthis disclosure and unless otherwise specified, “a” or “an” means “oneor more”.

The foregoing description of illustrative embodiments of the inventionhas been presented for purposes of illustration and of description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of theinvention. The embodiments were chosen and described in order to explainthe principles of the invention and as practical applications of theinvention to enable one skilled in the art to utilize the invention invarious embodiments and with various modifications as suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the claims appended hereto and theirequivalents.

What is claimed is:
 1. A method for creating metadevices, the methodcomprising: receiving, at a computing device, one or more boundaryconditions for a metadevice; processing, with an inverse-designalgorithm stored in a memory of the computing device, the one or moreboundary conditions to generate a metadevice structure design thatsatisfies the one or more boundary conditions; converting, by aprocessor of the computing device, the metadevice structure design intoa file that is compatible with an additive manufacturing device; andproviding the file of the metadevice structure design to the additivemanufacturing device.
 2. The method of claim 1, further comprisingcreating, by the additive manufacturing device, the metadevice thatsatisfies the one or more boundary conditions.
 3. The method of claim 2,wherein the additive manufacturing device comprises a three-dimensionalprinter.
 4. The method of claim 1, wherein the metadevice comprises anoptical metadevice, and wherein the optical metadevice is one of a lens,a polarization splitter, a filter, a bending device, a hologram, abeam-shaping device, an antenna, or an electromagnetic bandgap device.5. The method of claim 1, wherein the metadevice structure designcomprises a matrix.
 6. The method of claim 5, wherein the matrixrepresents a map of permittivity values and permeability values in atwo-dimensional space for the metadevice.
 7. The method of claim 6,wherein converting the metadevice structure design comprises convertingthe permittivity values into a matrix of binary values that representpresence or absence of material.
 8. The method of claim 7, whereinconverting the metadevice structure design further comprises convertingthe matrix of binary values into an image.
 9. The method of claim 8,wherein converting the metadevice structure design further comprisessmoothing edges of the image.
 10. The method of claim 8, whereinconverting the metadevice structure design further comprises vectorizingthe image.
 11. The method of claim 10, wherein converting the metadevicestructure design further comprises converting the vectorized image intoa full two-dimensional structure design.
 12. The method of claim 11,wherein converting the metadevice structure design further comprisesextruding the full two-dimensional structure design to generate athree-dimensional structure design having a thickness dimension.
 13. Themethod of claim 1, wherein the one or more boundary conditions includeat least one of focal distance, numerical aperture, angle of reflection,gain, directivity, permeability, and permittivity.
 14. A system forgenerating metadevices, the system comprising: a memory configured tostore an inverse-design algorithm; an interface configured to receiveone or more boundary conditions for a metadevice; and a processoroperatively coupled to the memory and the interface, wherein theprocessor is configured to: use the inverse-design algorithm to processthe one or more boundary conditions and generate a metadevice structuredesign that satisfies the one or more boundary conditions; convert themetadevice structure design into a file that is compatible with anadditive manufacturing device; and provide the file of the metadevicestructure design to the additive manufacturing device.
 15. The system ofclaim 14, further comprising the additive manufacturing device, whereinthe additive manufacturing device is configured to create the metadevicethat satisfies the one or more boundary conditions.
 16. The system ofclaim 14, wherein the metadevice structure design comprises a matrix.17. The system of claim 16, wherein the matrix represents a map ofpermittivity values and permeability values in a two-dimensional spacefor the metadevice.
 18. The system of claim 17, wherein conversion ofthe metadevice structure design comprises conversion of the permittivityvalues into the matrix, wherein the matrix includes binary values thatrepresent presence or absence of material.
 19. The system of claim 18,wherein conversion of the metadevice structure design further comprisesconversion of the matrix of binary values into an image.
 20. The systemof claim 19, wherein conversion of the metadevice structure designfurther comprises vectorization of the image.